Senators involved in the talks say the potential changes are meant to address concerns from the GOP caucus. A small but vocal wing remain adamantly opposed to the legislation, and several others have said they are wary about the impacts of the bill, lowering the prospects of passing it before the end of the year.

"I think all I should say is that we're taking into consideration the concerns that a lot of members in our conference had, the ones who are undecided, and we're seeing what we can do to accommodate them and getting more cosponsors," Grassley said on Thursday.

"We're discussing it in terms of how to increase the number of votes for it. There are lots of people with ideas about how to increase Republican votes but usually at the expensive of Democratic votes," he said. "It's a very delicate balance. It's a tricky equation."

Changes to the legislation could make it harder for senators to get the measure to Trump's desk before 2019. Senators have 10 session days before they are scheduled to leave for the year. During that time they're expected to tackle a Dec. 7 government funding bill, a farm bill and a debate on U.S.-Saudi relations.

Trump threw his support behind the Senate's criminal justice bill earlier this month, touting it as "tough on crime." The legislation would take a House-passed prison reform bill and add in four changes to sentencing laws, including lowering mandatory minimums for some drug-related felonies and retroactively applying the 2010 Fair Sentencing Act.

An administration official told The Hill that the White House asked GOP sponsors of the legislation to make changes addressing law enforcement concerns and, in turn, win over some of the more skeptical Republicans.

Grassley denied Thursday that the White House asked for changes to the bill.

One potential change would be to add the list of crimes that would exclude an individual from "earned time" credits that allow an inmate to take days off their sentence for completing certain programs or activities.

Conservatives have seized on opposition to the bill from the National Sheriffs' Association, which warned in a Nov. 15 letter to Senate leadership that the legislation amounted to a "social experiment."

"The current draft of the First Step legislation remains troubling to the leaders of law enforcement," the group wrote.

"Discussions are ongoing to see if we could come up with a consensus package or one that would at least get support from a substantial majority of Republicans," Cornyn said on Thursday.

He added that one suggested change would be to "embrace" the revisions recommend by the National Sheriffs' Association, which outlined five suggested changes in its letter to leadership. Cornyn said that could win over undecided Republicans like himself.

Senators and Vice President Pence discussed the Senate bill during a closed-door lunch this week, including debating both the merits of the legislation and when it should be taken up.

"I feel good about it. Can you make a few changes? Yes. If you do, does that get most people on board? Probably," Graham said this week. "If it doesn't happen this year, it's probably never going to happen."